Multiple aftershocks have been reported, and there is damage reported at the airport, according to news station 9News.
Water lines reportedly have broken at the airport.
There were no initial reports of major damage to buildings or injuries, said Utah Emergency Management spokesman Joe Dougherty.
Residents reported feeling shaking across a 100-mile area, with the heaviest impact in Salt Lake County, officials said.
Some residents ran from their homes and into the streets as they felt the earthquake shake buildings for 10 to 15 seconds.
The quake knocked pictures from walls and dishes from shelves, and people reported feeling it in the neighboring states of Colorado, Idaho, Wyoming and Nevada. Gov. Gary Herbert warned people to stay away from downtown Salt Lake City while crews assess the damage.
About 55,000 people lost electricity in the Salt Lake City area, said utility Rocky Mountain Power.
The road to the Salt Lake International Airport was closed, and officials asked people not to head to the airport.
It was the largest earthquake to hit Utah since a 5.9-magnitude quake shook southern Utah in 1992, according to Utah Emergency Management.
Most shaking was reported in the Salt Lake County area, near the epicenter in the Salt Lake City suburb of Magna, though effects of the quake were reported 80 miles away in the Utah city of Logan.
After the initial 5.7-magnitude quake struck at 7:09 a.m., the geological survey recorded four smaller quakes during the next 23 minutes, ranging in magnitude from 3.7 to 3.9.
Rich Barak of The Atlanta Journal-Constitution contributed to this report.